Some issues on models of black hole X-ray binaries

1. Some issues on models of black hole X-ray binaries Feng Yuan Shanghai Astronomical Observatory, Chinese Academy of Sciences

2. Outline • The accretion model for the hard state (XTE J1550-564 as an example) • Introduction to luminous hot accretion flows (LHAFs) • Explaining the X-ray emission of the luminous hard state of XTE J1550-564 with LHAFs • On the contribution of jet in the X-ray radiation of the hard state • The model for the quiescent state: jet-dominated?

3. ADAF and Its Critical Accretion Rate • The energy equation of ions in ADAFs: • For a typical ADAF (i.e., ), we have: • Since q- increases faster than q+ and qadv with increasing accretion rate, there exists a critical accretion rate of ADAFs, determined by (Narayan, Mahadevan & Quataert 1998): So advection is a cooling term Self-similar solution of ADAF

4. The dynamics of LHAFs: Basic Physics (I) • What will happen above the critical rate of ADAF? • Originally people think no hot solution exists; but this is not true • The energy equation of accretion flow: since: So we have:

5. The dynamics of LHAFs: Basic Physics (II) • An ADAF is hot because so the flow remains hot if it starts out hot. • When , up to another critical rate determined by We still have:  So again the flow will be hot if it starts out hot, i.e., a new hot accretion solution (LHAFs) exists between

6. Properties of LHAFs • Using the self-similar scaling law: • LHAF is more luminous than ADAFs since it corresponds to higher accretion rates and efficiency. • The entropy decreases with the decreasing radii. It is the converted entropy together with the viscous dissipation that balance the radiation of the accretion flow. • Since the energy advection term is negative, it plays a heating role in the Euler point of view. • The dynamics of LHAFs is similar to the cooling flow and spherical accretion flow.

7. The thermal equilibrium curve of accretion solutions: local analysis • Following the usual approach, we adopt the following two assumptions • we solve the algebraic accretion equations, setting ξto be positive (=1) and negative (=-0.1, -1, -10) to obtain different accretion solutions. Yuan 2003

8. Four Accretion Solutions Yuan 2001

9. LHAFs: Two Types of Accretion Geometry Hot accretion flow Type-I: Collapse into a thin disk See also Pringle, Rees & Pacholczyk 1973; Begelman, Sikora & Rees 1987 Type-II: Strong magnetic dissipation?

10. Global Solutions of LHAFs: Dynamics Yuan 2001 • α=0.3; • Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LHAF) 0.5 (long-dashed; type-II LHAF)

11. Global Solutions of LHAFs: Energetics Yuan 2001 • Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LHAF) 0.5 (long-dashed; type-II LHAF)

12. Stability of LHAFs • From the density profile, we know that LHAFs are viscously stable. • It is possibly convectively stable, since the entropy of the flow decreases with decreasing radius. • Outflow: the Bernoulli parameter is in general negative in LHAF, so outflow may be very weak. • LHAF is thermally unstable against local perturbations. However, at most of the radii, the accretion timescale is found to be shorter than the timescale of the growth of perturbation, except at the ``collapse’’ radius.

13. The thermal stability of LHAFs For type-I solution For type-II solution Yuan 2003

14. Application of LHAFs: the origin of X-ray emission in AGNs and black hole binaries • X-ray Luminosity. • The maximum X-ray luminosity an ADAF can produce is (3-4)%LEdd • X-ray luminosities as high as ~20% Eddington have been observed for the hard state (XTE J1550+564; GX 339-4) & AGNs. • An LHAF can produce X-ray luminosities up to ~10%LEdd • Spectral parameters • Assuming thermal Comptonization model for the X-ray emission, we can obtain (Te, τ) to describe the average spectrum of Seyfert galaxies • On the other side, we can solve the global solution for both ADAF and LHAF, to obtain the values of (Te, τ) • We find that an LHAF can produce better Te & τ than an ADAF (predicted Te too high compared to observation).

15. Modeling Luminous X-ray Sources: LHAFs better than ADAFs Yuan & Zdziarski 2004

16. An example: the 2000 outburst of XTE J1550-564 6% LEdd 3%LEdd 1%LEdd Yuan, Zdziarski, Xue & Wu 2007

17. LHAF Yuan, Zdziarski, Xue & Wu 2007

18. Yuan, Zdziarski, Xue & Wu 2007 The three dots show the E-folding energy of the three X-ray spectra shown in the previous figure.

19. Questions on LHAFs • Questions on theoretical side • Type-II LHAF is strongly thermally unstable at the transition radius, thus is it applicable in nature? • The range between the critical ADAF and type-I LHAF seems to be rather small • Questions on applications • It seems that an LHAF can only produce up to 10%LEdd X-ray luminosity, but many X-ray sources are likely more luminous • How to explain the very high state? (may related with the above item) • In some relatively luminous hard state, iron Ka line seems to be detected (but…)

20. Speculations on the Above Questions • the accretion flow is thermally unstable at the collapse radius. As a result, a two-phase accretion flow may be formed (e.g., prominence in solar corona; multi-phase ISM; Field 1965) . • The amount of clouds should be controlled by that the hot phase is in a ‘maximal’ LHAF regime • Such a two-phase configuration may correspond to a large range of rate; when the rate is higher, more matter will condense out. • when there are many clumps, they may form a thin disk. But photon bubble & clumping instabilities (Gammie 1998; Merloni et al. 2006) may make the disk clumpy again? Cold clumps Hot gas

21. The optical and X-ray light curves of XTE J1550-564 during its 2000 outburst. Secondary maxima No maximum in the X-ray! Jain et al. 2001, ApJ

22. Secondary Maximum: the contribution of the jet Jet emission Yuan, Zdziarski, Xue & Wu 2007

23. Observed radio---X-ray correlation Radio/X-ray correlation of GX 339-4; from Corbel et al. 2003, A&A

24. Radio-X-ray correlation and the quiescent state • The optically-thin synchrotron emission , while the Comptonization from the hot accretion flow • With the decrease of accretion rate, the X-ray emission of the system will be dominated by the jet • Thus a change of the radio---X-ray correlation is expected, from AB to CD. The critical luminosity is: • The X-ray emission of the quiescent state (below the above critical luminosity) should be dominated by jets

25. Radio-X-ray correlation in the larger regime of luminosity Yuan & Cui 2005, ApJ The change of the radio—X-ray correlation from hard to quiescent states

26. Test the prediction Wu, Yuan, & Cao 2007